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For each of the graphs given in Fig. select the equation whose graph it is from the choices given below :
$(a)$ For Fig. $(i)$,
$(i)$ $x+y=0$ $(ii)$ $y=2 x$ $(iii)$ $y=x$ $(iv)$ $y=2 x+1$
$(b)$ For Fig. $(ii)$,
$(i)$ $x+y=0$ $(ii)$ $y=2 x$ $(iii)$ $y=2x+4$ $(iv)$ $y=x-4$
$(c)$ For Fig. $(iii)$,
$(i)$ $x+y=0$ $(ii)$ $y=2 x$ $(iii)$ $y=2x+1$ $(iv)$ $y=2 x-4$
Solution
$(a)$ In Fig. $(i)$, the points on the line are $(-1, \,-2)$, $(0,\, 0)$, $(1,\, 2)$. By inspection, $y = 2x$ is the equation corresponding to this graph. You can find that the $y$ – coordinate in each case is double that of the $x$ – coordinate.
$(b)$ In Fig. $(ii)$, the points on the line are $(-2,\, 0)$, $(0,\, 4)$, $(1,\, 6)$. You know that the coordinates of the points of the graph (line) satisfy the equation $y = 2x + 4.$ So, $y = 2x + 4$ is the equation corresponding to the graph in Fig. $(ii)$.
$(c)$ In Fig. $(iii)$, the points on the line are $(-\,1, \,-\,6)$, $(0, \,-\,4)$, $(1, \,-\,2),$ $(2,\, 0)$. By inspection, you can see that $y = 2x -4 $ is the equation corresponding to the given graph (line).
